An Algebraic Semantics for Possibilistic Logic

TL;DR

This paper introduces an algebraic semantics for possibilistic logic using a Pavelka-like formulation with new connectives, providing a dynamic, algebraic framework with a sound and complete calculus.

Contribution

It presents a novel algebraic semantics for possibilistic logic with enriched connectives and a Gentzen calculus, enhancing the understanding of information combination.

Findings

The semantics is based on the lattice of possibility functions.

A Gentzen calculus is developed and proved sound and complete.

The approach offers a dynamic perspective on possibilistic logic.

Abstract

The first contribution of this paper is the presentation of a Pavelka - like formulation of possibilistic logic in which the language is naturally enriched by two connectives which represent negation (eg) and a new type of conjunction (otimes). The space of truth values for this logic is the lattice of possibility functions, that, from an algebraic point of view, forms a quantal. A second contribution comes from the understanding of the new conjunction as the combination of tokens of information coming from different sources, which makes our language "dynamic". A Gentzen calculus is presented, which is proved sound and complete with respect to the given semantics. The problem of truth functionality is discussed in this context.